Brett Kotschwar (Arizona State University)

Title: Backward propagation of warped-product structures under the Ricci flow and asymptotically conical shrinkers

Abstract: We establish sufficient conditions for a locally-warped product structure to propagate backward in time under the Ricci flow. As an application, we show that if a gradient shrinking soliton is asymptotic to a cone whose cross-section is a locally warped product of Einstein manifolds, the soliton must itself be a warped product over the same manifolds.